2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108899We prove that every smooth action of Z^k, k>1, on the (k+1)-dimensional torus homotopic to an action by hyperbolic linear maps preserves an absolutely continuous measure. This is a first known result concerning abelian groups of diffeomorphisms where existence of an invariant geometric structure is obtained from homotopy data.28 pagesDynamical Systems37C40 (Primary) 37D25, 37C85 (Secondary)text